This paper assesses the stochastic convergence of relative CO 2 emissions within 28 OECD countries over the period 1950â€“2013. Using the local Whittle estimator and some of its variants we assess whether relative per capita CO 2 emissions are long memory processes which, although highly persistent, may revert to their mean/trend in the long run thereby indicating evidence of stochastic convergence. Furthermore, we test whether (possibly) slow convergence or the complete lack of it may be the result of structural changes to the deterministics of each of the relative per-capita emissions series by means of the tests of Berkes et al. (Ann Stat 1140â€“1165, 2006) and Mayoral (Oxford Bull Econ Stat 74(2):278â€“305, 2012). Our results show relatively weak support for stochastic convergence of CO 2 emissions, indicating that only between 30 and 40% of the countries converge to the OECD average in a stochastic sense. This weak evidence disappears if we enlarge the sample to include 4 out of the 5 BRICS, indicating that our results are not robust to the inclusion of countries which are experiencing rates of growth which are far larger than those of the OECD members. Our results also decisively indicate that a slow or lack of convergence is not the results of a structural break in the relative CO 2 emissions series.